An electronic imaging system typically produces a signal output corresponding to a viewed object by spatially sampling an image of the object in a regular pattern with a fixed, regular array of photosensitive picture elements, such as, for example, with a charge-coupled device (CCD) solid-state image sensor, a charge injection device, or a vidicon. In such imaging systems, it is well-known that detail components in the object which contain frequencies too high to be analyzed within the sampling interval of the sensor contribute to the amplitudes of lower frequency components, and thereby produce imaging errors commonly referred to as aliasing or undersampling artifacts. In particular, if spatial detail being imaged contains a high frequency component of a periodicity smaller than the pitch (periodicity) of each neighboring photosensitive picture element of the solid state image sensor, the subsequent detection of this high frequency component tends to result in a spurious signal due to aliasing. Such aliasing artifacts severely reduce the quality of video or still images.
The pitch (periodicity) of the elements in a photosensitive picture element array is the center-to-center distance of the elements in the array. The sampling frequency of the sensor is 1/(sensor pitch) and the Nyquist frequency of the sensor is 1/2 the sampling frequency. It is well known in the prior art that if the spatial frequency content of the scene image that falls on the sensor exceeds the Nyquist frequency for the sensor, aliasing will result. The high frequency information will appear to be low frequency image data in the sampled image. Color cameras, particularly single sensor cameras, have a color filter array that includes several different colors, thereby reducing the sensor sampling frequency for each color and making the sensor more susceptible to aliasing. Moreover, the sampling frequency and the Nyquist frequency may not be equally related for all colors because the color filter array may not have equal numbers of pixels in each color plane, which leads to colored aliasing artifacts in response to neutral high frequency image content. This effect substantially reduces image quality.
There are many well-known methods for reducing aliasing from a two-dimensional array of photosites. These all involve optically limiting the scene image frequency content to spatial frequencies below the Nyquist frequency by blurring the image in several dimensions in a controlled manner. In general, an electronic imaging system can minimize aliasing if its optical section has a frequency response that cuts off, or filters out, the higher frequency content of the object. As a result, the optical section generally employs an optical low pass filter to substantially reduce the high frequency component contained in the spatial detail of the image received by the image sensor. It is thus well-known in the prior art that the design of electronic imaging systems involves a trade-off between image sharpness and the susceptibility of the imaging system to aliasing distortions or undersampling artifacts.
The electronic imaging systems employed in digital cameras typically have an optical blur filter, also known as an anti-aliasing filter, over the sensor to provide the low pass filtering and to prevent aliasing in the image. These filters are typically made of quartz crystal and take advantage of the birefringent properties of quartz. A single layer of quartz will produce two image points in the image for a single point in the object. Since digital cameras have a two-dimensional CCD array, an optical low pass filter that produces two image points in each direction for a given object point is preferred. A common type of such filter consists of several layers of quartz that produce a four-spot square pattern. This pattern suppresses aliasing more on the diagonal orientation than on the x- and y-axis but the x and y suppression is equal, and the suppression on the diagonals is also equal.
A typical birefringent blur filter uses three plates of quartz aligned, for example, to convert a single image point spread function to a square pattern of four point spread functions arrayed at the four corners of the square. A typical example of such a filter is described in Japanese patent application No. 52-66449. Other methods use diffraction to increase the size of the point spread function, e.g., see U.S. Pat. No. 4,178,611, which describes a two-dimensional grating having a triangular wave cross-sectional configuration with respect to two directions. In U.S. Pat. No. 4,878,737, two periodic structures are provided on a surface of a transparent substrate so as to form a regularly arranged pattern of projections, each in the form of a frustrum of a pyramid.
It is also known that a single polygonal prism placed in the aperture of an optical system acts as an optical low-pass filter (e.g., see U.S. Pat. No. 3,821,795). For example, a weak pyramid can be used as taught by U.S. Pat. No. 4,989,959 and a weak axicon can be used as taught by U.S. Pat. No. 5,322,998. (An axicon is herein taken to mean a conical shape, or a substantially conical shape, such as a truncated cone.) Both the weak pyramid and the weak axicon operate similarly, the pyramid producing four spots from a single point at certain focal distances and the axicon producing a ring at certain focal distances. ("Weak" as used herein refers to pyramid or axicon angles of generally less than five minutes of arc.) The ring reduces the image modulation to zero at spatial frequencies of 1/(diameter of the ring) and the pyramid reduces the image modulation to zero at spatial frequencies of 1/(spot spacing).
The pyramid and axicon filters work best if they are placed at the system stop or at an image of the stop if a real image is accessible. Retrofocus lens designs are very common in video camera designs because they have sufficient backfocus to clear the cover glass of the CCD sensor. The pyramid and axicon filters do not work well when placed in front of a retrofocus lens since the ray bundles for most off axis points pass through only one side of the axicon or one facet of the pyramid. For small angles off axis, the amount of blur will thus be field dependent and there will be almost no blur at all for bundles that pass through only one side of the axicon or one facet of the pyramid.
Furthermore, the pyramid and axicon filters only work well for flat objects where the system focus can be controlled. The objective is to maintain the blur effect at all focal lengths, and the problem with a single polyhedral or conical prism is that the blur effect is eliminated if the user refocuses the optical system incorporating the blur filter. Consequently, the effects of both filter types can be mitigated almost completely by adjusting the system focus. Furthermore, if the object is not flat, then one plane will be at the focal distance that has the desired point spread function and other planes will have smaller and larger point spread functions.
The axicon filter adds a weak conical aberration to the pupil wavefront in a well corrected lens design, and the pyramid filter adds a weak pyramidal aberration. Defocus adds a spherical shape to the pupil wavefront. A weak sphere can be subtracted from the axicon or pyramid wavefront by refocusing the system. The resulting aberration will be almost too small to notice and composed mostly of spherical aberration. The angle of the axicon or the face angles of the prism are typically small. They are chosen so that the separation of the point spread function is on the order of the pitch of the photosite array if zero modulation at the Nyquist frequency is desired. If a different zero is desired, the separation can be chosen for this spatial frequency.
The aberration added by the blur filter is very small and the size of the point spread function is not very much larger than the unaberrated point spread function at the focal plane with the smallest rms point spread function. It is possible to increase the axicon or pyramid angle until the point spread function minimum size is large enough to reduce modulation of high frequency content of the image. The dominant aberration is spherical which produces a point spread function with a bright center and a large skirt. The skirt reduces the modulation at low frequencies and the bright center maintains modulation at high frequency. This is clearly not the optimum filter. Ideally the cutoff should be sharp at the Nyquist frequency without a reduction in the modulation at low spatial frequencies. What is needed is an optical blur filter that maintains the blur effect despite refocusing without reducing modulation at low spatial frequencies.